Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | #90186⋊C3 |
| Fitting | C2×C7×C22⋊C4 ⋊ C2×C3 |
| Hall | #90186 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ #551 |
| Sylow | C7 ⋊ C3×#551 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
Polycyclic presentation:
2^4,3,2^2,7|c^2=f,b^a=bg,d^a=df,h^a=h^6,c^b=cg,d^c=dg,h^e=h^295 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×#551, #72277073, #72277221, … |
| maximal normal subgroup of | AGL(1,𝔽7)×#551, #72277073, #72277221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6518);